By an argument based on Newtonian physics. There are no direct observations that show the Earth to be the center of the solar system. Kepler showed that the orbit of Mars was an ellipse, not a circle as required by Copernicus' heliocentric model. Only by allowing planets and the Sun to travel on extremely complex paths through space could you make a geocentric model of the universe. Prior to the advent of Newtonian mechanics, there was no reason to believe that planets could not travel on such complex paths, but after universal gravitation was discovered, and integrated into Newtonian mechanics, this possibility came to an end. The Earth, being smaller in mass than the Sun, could not be at the center of the orbit of a more massive body such as the Sun. Also, the planets now became physical, massive, objects, and as such any accelerations they feel much come from the application of an external force to cause them to move in complex orbits as required by geocentric theory. Placing the massive Sun at the center, and letting the whole system respond to the Sun's gravitational field, led to simple elliptical paths, and no complex external forces other than gravity from the Sun acting in strength with the inverse-square of a planet's distance from the Sun. What could be simpler.